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In this video, we will learn how to convert metric units of capacity.
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These will include cubic centimeters, cubic decimeters, cubic meters, and milliliters and liters.
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We will begin by looking at some key definitions and conversions.
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Your teacher might well have used the words volume and capacity.
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Whilst these are often interchangeable in mathematical questions, there are some subtle differences between them.
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Firstly, volume is the amount of space taken up by an object, while capacity is the measure of an object’s ability to hold a substance like a solid, a liquid, or a gas.
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We tend to get asked questions about the volume of a three-dimensional shape, such as a cuboid or a cylinder.
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However, we would be asked to calculate the capacity of a fish tank.
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This is because we would be looking to calculate the amount of water the fish tank could hold.
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Volume is measured in cubic units, such as centimeters cubed, decimeters cubed, or meters cubed, whereas capacity can be measured in units such as gallons, pints, liters, and milliliters.
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In this video, we will deal with liters and milliliters as these are the metric units.
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We will now look at some key conversions between the units.
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When dealing with volume, we firstly need to consider meters, decimeters, and centimeters.
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The prefix deci- denotes a factor of one-tenth and comes from the Latin “decimus” meaning tenth.
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A decimeter is therefore one-tenth of a meter.
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In the same way, centi- comes from the Latin “centum” and one centimeter is one-hundredth of a meter.
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These prefixes mean that there are 100 centimeters in one meter and 10 centimeters in one decimeter.
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We can see how this corresponds to the volume conversions by firstly considering a one-centimeter cube.
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This has a volume of one cubic centimeter.
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A one-decimeter cube will have dimensions 10 centimeters by 10 centimeters by 10 centimeters.
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Multiplying 10 by 10 by 10 gives us 1000.
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Therefore, one cubic decimeter is equal to 1000 cubic centimeters.
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We could repeat this process to convert from cubic centimeters to cubic meters or cubic decimeters to cubic meters.
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There are three conversions we need to remember.
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1000 cubic centimeters is equal to one cubic decimeter.
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1000 cubic decimeters is equal to one cubic meter.
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And finally, 1000000 cubic centimeters is equal to one cubic meter.
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We can therefore convert from cubic centimeters to cubic decimeters by dividing by 1000 and from cubic decimeters to cubic meters by dividing by 1000.
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If we need to convert in the opposite direction, we need to multiply by 1000.
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When dealing with capacity, 1000 milliliters is equal to one liter.
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This is because the prefix milli- means one-thousandth.
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Once again, to convert from milliliters to liters, we would divide by 1000 and, from liters to milliliters, multiply by 1000.
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It is also important to know that we can convert from volume to capacity using the fact that one cubic centimeter is equal to one milliliter.
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This in turn leads to the fact that one cubic decimeter is equal to one liter, and one cubic meter is equal to 1000 liters.
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We will now use these conversions to solve some problems involving volume and capacity.
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Write in cubic decimeters 5625 cubic centimeters.
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We begin by recalling that the prefix deci- means one-tenth and centi- means one-hundredth.
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This means that a decimeter is one-tenth of a meter and a centimeter is one-hundredth of a meter.
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There are 10 centimeters in one decimeter.
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By considering the two identical cubes, one in decimeters and one in centimeters, we can see that one cubic decimeter is equal to 1000 cubic centimeters.
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This means that, in order to convert from cubic centimeters to cubic decimeters, we need to divide by 1000.
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The calculation required in this question is 5625 divided by 1000.
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When dividing by 1000, we move all our digits three places to the right.
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5625 cubic centimeters in cubic decimeters is 5.625.
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Our next question involves ordering capacities and volumes.
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Arrange in ascending order: 1800 cubic centimeters, 6.8 cubic decimeters, 1.3 cubic decimeters, and 1100 cubic centimeters.
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As we are asked to arrange the values in ascending order, we need to do so from least to greatest.
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In order to do this, we need to ensure that our units are the same.
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Currently, we have two in cubic centimeters and two in cubic decimeters.
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We recall that there are 1000 cubic centimeters in one cubic decimeter.
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This means that, in order to convert from cubic centimeters to cubic decimeters, we need to divide by 1000.
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To convert from cubic decimeters to cubic centimeters, we multiply by 1000.
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This is the method we will use in this question.
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We will convert 6.8 and 1.3 cubic decimeters into cubic centimeters.
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When multiplying by 1000, we move all the digits three places to the left.
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So 6.8 multiplied by 1000 is 6800.
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In the same way, 1.3 multiplied by 1000 is 1300.
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We now have all four values in cubic centimeters.
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The smallest or least value is 1100 cubic centimeters.
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The next smallest value was 1300 cubic centimeters, which is the same as 1.3 cubic decimeters.
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Next, we have 1800 cubic centimeters.
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And finally, the largest or greatest value is 6800 cubic centimeters or 6.8 cubic decimeters.
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In order to write any set of values in ascending or descending order, we firstly need to ensure that all the units are the same.
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Our next question involves conversion and an addition calculation.
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Write the answer in cubic centimeters: 4.3 cubic decimeters plus 5950 cubic centimeters.
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We immediately notice in this question that our two values have different units.
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As we’ve been asked to write the answer in cubic centimeters, we need to convert our first value from cubic decimeters to cubic centimeters.
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There are 1000 cubic centimeters in one cubic decimeter.
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This means that, in order to convert from cubic centimeters to cubic decimeters, we would divide by 1000.
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To convert the other way as we need to in this case, we need to multiply by 1000.
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4.3 multiplied by 1000 is 4300.
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So 4.3 cubic decimeters is the same as 4300 cubic centimeters.
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We now need to add 4300 and 5950.
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This is equal to 10250.
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The answer to the question 4.3 cubic decimeters plus 5950 cubic centimeters in cubic centimeters is 10250.
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We could convert this answer into cubic decimeters by dividing by 1000.
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This would give us an answer of 10.25 cubic decimeters.
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We will now move on to look at some questions involving milliliters and liters.
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If five drops of water fill up a volume of five milliliters, then how many drops would fill up a volume of seven liters?
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We’re told in the question that five drops of water are equal to five milliliters.
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This means that one drop would be equal to one milliliter.
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We need to calculate the number of drops in seven liters.
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The prefix milli- means one-thousandth.
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So a milliliter is one-thousandth of a liter.
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We can therefore use the calculation that 1000 milliliters is equal to one liter.
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Multiplying both sides of this by seven gives us 7000 milliliters is equal to seven liters.
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We can therefore conclude that as five drops of water filled up a volume of five milliliters, 7000 drops of water will fill up a volume of seven liters.
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If the capacity of a tin is 42.4 liters, what is its volume in cubic decimeters?
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In order to answer this question, we need to recall some of our conversions.
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The prefixes deci-, centi-, and milli- mean one-tenth, one-hundredth, and one-thousandth, respectively.
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This means that a decimeter is one-tenth of a meter.
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A centimeter is one-hundredth of a meter.
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And a milliliter is one-thousandth of a liter.
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As there are 10 centimeters in one decimeter, we can calculate the number of cubic centimeters in one cubic decimeter by cubing both sides.
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10 cubed is equal to 1000, so there are 1000 cubic centimeters in one cubic decimeter.
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We know from the prefix milli- that there are 1000 milliliters in one liter.
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We now need to recall how we can convert from units of capacity to units of volume.
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One milliliter of capacity is equal to one cubic centimeter of volume.
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This means that one liter of capacity must be equal to one cubic decimeter of volume.
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As the ratio of cubic decimeters to liters is one to one, then 42.4 liters will be equal to 42.4 cubic decimeters.
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We will now summarize the key points from this video.
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It is important to remember that the words volume and capacity are often interchangeable in exam questions.
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It is important to note, though, that volume is the amount of space taken by an object, whereas capacity is an object’s ability to hold a substance such as a solid, liquid, or gas.
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Volume can be measured in cubic centimeters, cubic decimeters, and cubic meters.
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Capacity, on the other hand, can be measured in the metric units of milliliters or liters.
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The prefixes centi-, deci-, and milli- can be used to help us work out our conversions.
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A centimeter is one-hundredth of a meter, a decimeter is one-tenth of a meter, and a milliliter is one-thousandth of a liter.
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As our units for volume were cubic units, we have the following conversions.
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1000 cubic centimeters is equal to one cubic decimeter.
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We also have 1000 cubic decimeters is equal to one cubic meter.
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Combining these two conversions tells us that there are 1000000 cubic centimeters in one cubic meter.
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When dealing with capacity, there are 1000 milliliters in one liter.
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When converting between units of volume and units of capacity, we can use the fact that one cubic centimeter of volume is the same as one milliliter of capacity.
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This in turn leads us to the fact that one cubic decimeter is equal to one liter.
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There are 1000 liters in one cubic meter.
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Recalling these conversions or remembering how to calculate them allows us to convert between different units by multiplying and dividing by 1000.
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These are some of the key points to remember when dealing with metric units of volume and capacity.